diff --git a/pytorch_lightning/callbacks/gpu_stats_monitor.py b/pytorch_lightning/callbacks/gpu_stats_monitor.py
index ace69b0234..498b536994 100644
--- a/pytorch_lightning/callbacks/gpu_stats_monitor.py
+++ b/pytorch_lightning/callbacks/gpu_stats_monitor.py
@@ -23,7 +23,7 @@ import os
 import shutil
 import subprocess
 import time
-from typing import Dict, List, Tuple
+from typing import Any, Dict, List, Tuple
 
 from pytorch_lightning.callbacks.base import Callback
 from pytorch_lightning.utilities import DeviceType, rank_zero_only
@@ -101,7 +101,7 @@ class GPUStatsMonitor(Callback):
             'temperature': temperature
         })
 
-    def on_train_start(self, trainer, *args, **kwargs):
+    def on_train_start(self, trainer, pl_module) -> None:
         if not trainer.logger:
             raise MisconfigurationException('Cannot use GPUStatsMonitor callback with Trainer that has no logger.')
 
@@ -113,12 +113,14 @@ class GPUStatsMonitor(Callback):
 
         self._gpu_ids = ','.join(map(str, trainer.data_parallel_device_ids))
 
-    def on_train_epoch_start(self, *args, **kwargs):
+    def on_train_epoch_start(self, trainer, pl_module) -> None:
         self._snap_intra_step_time = None
         self._snap_inter_step_time = None
 
     @rank_zero_only
-    def on_train_batch_start(self, trainer, *args, **kwargs):
+    def on_train_batch_start(
+        self, trainer, pl_module, batch: Any, batch_idx: int, dataloader_idx: int
+    ) -> None:
         if self._log_stats.intra_step_time:
             self._snap_intra_step_time = time.time()
 
@@ -136,7 +138,9 @@ class GPUStatsMonitor(Callback):
         trainer.logger.log_metrics(logs, step=trainer.global_step)
 
     @rank_zero_only
-    def on_train_batch_end(self, trainer, *args, **kwargs):
+    def on_train_batch_end(
+        self, trainer, pl_module, outputs: Any, batch: Any, batch_idx: int, dataloader_idx: int
+    ) -> None:
         if self._log_stats.inter_step_time:
             self._snap_inter_step_time = time.time()
 
diff --git a/pytorch_lightning/callbacks/model_checkpoint.py b/pytorch_lightning/callbacks/model_checkpoint.py
index 5f0318e7ac..a1a44fd70b 100644
--- a/pytorch_lightning/callbacks/model_checkpoint.py
+++ b/pytorch_lightning/callbacks/model_checkpoint.py
@@ -215,7 +215,9 @@ class ModelCheckpoint(Callback):
         self.__resolve_ckpt_dir(trainer)
         self.save_function = trainer.save_checkpoint
 
-    def on_train_batch_end(self, trainer, *args, **kwargs) -> None:
+    def on_train_batch_end(
+        self, trainer, pl_module, outputs: Any, batch: Any, batch_idx: int, dataloader_idx: int
+    ) -> None:
         """ Save checkpoint on train batch end if we meet the criteria for `every_n_train_steps` """
         if self._should_skip_saving_checkpoint(trainer):
             return
@@ -225,7 +227,7 @@ class ModelCheckpoint(Callback):
             return
         self.save_checkpoint(trainer)
 
-    def on_validation_end(self, trainer, *args, **kwargs) -> None:
+    def on_validation_end(self, trainer, pl_module) -> None:
         """
         checkpoints can be saved at the end of the val loop
         """